With regard to dependents, all are eligible for enrollment in the postdoc insurance plans. If your wife currently has coverage at her institution, you could waive coverage for her and only enroll your child. Once your wife's coverage terminates, she would then be eligible to enroll as a dependent on the postdoc plan (loss of coverage is seen as a "qualifying event").

In most cases, the department pays 100% of your insurance costs (including dependents). Exceptions to this rule are: 1) when you select the more premium PPO medical option, at which time you pay $30/60/90 per month depending on the number of your dependents ($90 in the case of adding a spouse & child); and 2) if your funding source is an individual fellowship. With the latter, departments are still encouraged to meet the same contribution levels as with the postdoc "employee," but in a handful of cases, they may request that you pay a portion of the premiums.

Another solution postdoc students may want to look at when deciding on affordable health insurance is the many student insurance sites. I found when I did my undergrad that I could actually get cheaper insurance going through a student insurance company than with the school. I am looking at UCLA for graduate work and will post here if this is the same situation.